(Compound Inequalities)

(B). - 7 ≤ x < 12

Step-by-step explanation:

- 7x - 50 ≤ - 1 ⇔ - 7x ≤ 49 ⇒ x ≥ - 7  

and

- 6x + 70 > - 2 ⇔ - 6x > - 72 ⇒ x < 12

- 7 ≤ x < 12

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions